Question

How would you "remove the discontinuity" of f ? In other words, how would you define

f(4)
in order to make f continuous at 4?
f(x) =
x2 − x − 12
x − 4

Answer 1

there is a hole at x=4 because the top factors to (x-4)(x+3)
in the end we get

f(x)=(x-4)(x+3)/(x-4)
the (x-4) cancels out and we get
f(x)=x+3
so baiscally f(x) is y=x+3 but with a hole at (4,7)


one way is to make a piecewise function defined as(x^2-x-12)/(x-4) for all x≠4 and defined as 7 for x=4

or, to just do f(x)=x+3